Recruitment variability and stochastic population growth of the soft-shell clam, Mya arenaria

Variability in recruitment is a striking feature of the life histories of most marine invertebrates and many fishes. The distribution of recruitment is typically lognormal rather than normal. It has been conjectured that such variation plays a major role in population growth of these species, but no complete stochastic demographic analysis has ever been reported. Here, we developed a set of deterministic and stochastic models for the clam, Mya arenaria. We constructed a size-classified, periodic matrix model to describe seasonal population dynamics, based on a mark-recapture study in Barnstable Harbor, MA, USA. In the deterministic model, an equilibrium recruitment rate of ERR=19.4 recruits per adult was required to maintain constant population size. Periodic elasticity analysis showed that, at the ERR, fertility and larval survival accounted for 99% of the population growth rate λ. In a stochastic model with lognormally distributed recruitment, the stochastic growth rate log⁡λs increased with increases in either E(log⁡R) or SD(log⁡R). The positive effect of SD(log⁡R) is due to the highly skewed nature of the lognormal distribution. Variation in population size increases dramatically with increases in SD(log⁡R), which makes it difficult to predict future population size. If variability in recruitment is high, quasi-extinction is nearly certain even when log⁡λs is well above zero. Stochastic elasticity analysis shows that the contribution of adult growth and survival to λs increases dramatically when recruitment is variable. These results suggest that, for marine invertebrates with a lognormally distributed recruitment pattern, the amount of uncertainty in recruitment should be positively associated with adult life span.